There is an implicit, widely-held sense that the detail in proofs should scale with the expected training of the people who will be reading them. If your intended audience has internalized their field so well that the expansion and checking happens completely automatically and subconsciously, more power to them - but on the other end of the scale you have the proof that the square root of two is irrational, or this one about interior angles. Other than machine-aided proofs the most thoroughly expanded you ever see anything is in highschool geometry!
So, what justifies this scheme? I would say that once you have seen a technique used in full detail, you don't need to see the detail elsewhere because there's a meta-theorem in your head that applies to every case where things line up in a pattern where the technique works. Slowly this replaces your natural intuition.
So, what justifies this scheme? I would say that once you have seen a technique used in full detail, you don't need to see the detail elsewhere because there's a meta-theorem in your head that applies to every case where things line up in a pattern where the technique works. Slowly this replaces your natural intuition.